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The efficiency of algorithms is of crucial importance in many applications. In the course Data Structures you have learned how to mathematically analyze efficiency, how to use design techniques like divide-and-conquer,​ and you have seen efficient algorithms and data structures for basic problems such as sorting and searching. In the course Algorithms we will take this one step further, by studying more advanced design techniques and algorithms, and by studying other aspects of efficiency. Many of the topics that are covered concern optimization problems, where one wants to find not just some solution to a problem but an optimal solution. The course consists of three parts.

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**Algorithmic techniques for optimization.** In this part of the course we study three general techniques for solving optimization problems: backtracking,​ dynamic programming,​ and greedy algorithms. Backtracking can be applied to more or less all problems but it generally yields very slow algorithms, a greedy approach can be applied to few problems but it generally gives very fast algorithms, and dynamic programming lies in between.

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**Graph algorithms.** The second part of the course deals with algorithms for optimization problems on graphs: computing shortest paths, computing maximum flows, and finding so-called matchings.

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**Selected topics.** In the third part of the course we study the limitations of traditional algorithm design and analysis. We consider problems for which it seems impossible to design efficient algorithms and introduce the concept of NP-hardness (which formalizes this). We introduce linear programming,​ and see how optimization problems can be formulated as linear programs.

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===== Literature =====

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The course is based on the following book, which is the same book as used in the course Data Structures:

During the lectures hours, the basic theory will be taught and plenary feedback on the homework exercises may be given.

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The tutorial hours are used either for working on and asking questions about the homework assignments,​ for discussion of the solutions to the homework exercises, and for individual feedback. Tutorial groups will be made during the first week of classes.

The final grade will be based on two components: homework exercises and an exam.

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There are six sets of homework exercises. The deadlines for these homework sets can be found in the schedule. For each set you can get up to 10 points. Your final score for the homework assignment is calculated as follows:

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* take the sum of the 6 homework scores, subtract the lowest score among the 5 sets that do not deal with NP-completeness,​ and divide the result by 5.

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In other words, the grade for the set on NP-completeness always counts, but the worst-scoring grade for the remaining 5 sets does not count.

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On the exam you can score up to 10 points.

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The final grade is determined as follows:

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* If your exam grade is at least 5.0, your final grade is the rounded average of your homework grade and your exam grade. In other words: if your exam grade is at least 5.0, you pass if your homework grade is at least 11 minus your exam grade.

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* If your exam grade is less than 5.0, your final grade is the minimum of a 5 and the rounded average of your homework grade and your exam grade. Therefore, if your exam grade is less than 5.0, you fail the course in any case.

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===== Homework assignments =====

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Homework exercises must be done individually,​ that is, you must write the solution by yourself. Handwritten solutions and solutions made in pairs will not be graded and automatically get a score of 0 (zero) points. Do not search the internet for solutions. Solutions copied from the internet, or from other students, automatically get 0 points; copying is considered fraud, and students who copy may be reported to the exam committee.

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You are advised to prepare the solutions using LaTeX: this usually gives much nicer results than Word, especially for mathematical formulas. Some information about LaTeX can be found on the [[https://​www.win.tue.nl/​aga/​teaching/​2IL50/​|course website of Data Structures]]. For describing algorithms you can use the package [[http://​www.win.tue.nl/​~hermanh/​lib/​exe/​fetch.php?​media=2il45:​algo.zip|algo]],​ [[http://​www.ctan.org/​pkg/​algorithm2e|algorithm2e]],​ or [[http://​www.ctan.org/​pkg/​clrscode3e|clrscode3e]] (other packages exist as well). For drawing figures, you can use [[http://​ipe.otfried.org/​|Ipe]] or [[https://​www.yworks.com/​en/​products_yed_download.html|yEd Graph Editor]], for example.

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In the tutorials you can ask for help on the homeworks. You can even show your solutions (including typeset solutions that you are planning to hand in), and ask for feedback e.g. about the level of detail of your solution, or about whether the general idea of your solution is correct.

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===== Schedule =====

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The schedule below is tentative and may be adapted during the course. Note that, for your convenience,​ the dates are not completely in chronological order: the deadline for the homework is listed after the last tutorial dedicated to that homework.